What is the integral of (ln(x^4))/(x^7) ?

The integral of (ln(x^4))/(x^7) is 4(-(ln(x))/(6x^6)-1/(36x^6))+C

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integral of (ln(x^4))/(x^7)

\int \frac{ln ( x ^{4} )}{x ^{7}} d x

4 (- \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}}) + C

Solution steps

\int \frac{ln ( x ^{4} )}{x ^{7}} d x

Simplify

ln (x^{4}) : 4 ln (x)

= \int \frac{4 ln ( x )}{x ^{7}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int \frac{ln ( x )}{x ^{7}} d x

Apply Integration By Parts

: - \frac{ln ( x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x

= 4 (- \frac{ln ( x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x)

\int - \frac{1}{6 x ^{7}} d x = \frac{1}{36 x ^{6}}

= 4 (- \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}})

Add a constant to the solution

= 4 (- \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}}) + C

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What is the integral of (ln(x^4))/(x^7) ?
The integral of (ln(x^4))/(x^7) is 4(-(ln(x))/(6x^6)-1/(36x^6))+C